Resistance networks exhibiting useful properties are used in many aspects of electrical metrology for: the realisation of electrical measurement standards; the evaluation of those standards; and the evaluation of electrical measuring equipment. One such family of networks in common use is the 4-terminal series-parallel build-up resistors known as Hamon resistors. The basic design of the Hamon resistor was proposed by Hamon in 1954--see B V Hamon, "A 1-100 ohm build-up resistor for calibration of standard resistors", J Sci Instru, vol 31, pp 450-453, December 1954. Three of the four key principles that Hamon brought together in his resistor network were known for some time. The principles exploited by Hamon resistor are:
The Four-Terminal Resistor: Electrical resistances drawn in most engineering texts have two terminals. In such a resistor it is impossible to electrically discriminate between the resistor itself and the resistance in the two lead wires connected to it. This severely limits the attainable accuracy in many applications. For high accuracy work four-terminal resistors are used. These resistors have two terminals through which the current is passed, and two terminals where the voltage is measured. The ratio of the voltage to current, the resistance, is independent of all of the four lead resistances. This principle is probably due to Lord Kelvin.
Equal Resistors Connected in Series and Parallel to Realise Accurate Resistance Ratios: It was known that the resistance of N nominally equal value resistors in series is equal to N squared times the resistance of the N resistors in parallel. Further, if the values of the N resistors are adjusted to equality within a given tolerance then the accuracy of the ratio of the series to parallel resistances is accurate to the square of the tolerance. For example, 10 nominally equal 10 ohm resistors matched to within 1 part in 1000 (0.1%) may be connected in series to make a 100 ohm resistance, or in parallel to make a 1 ohm resistance. It can be shown that the ratio of the two resistances so made is accurate to 1 part in 1 000 000 (0.00001%). This principle is probably due to Lord Rayleigh.
The Four-Terminal Junction: Prior to the publication of Hamon's paper, Rayleigh's series-parallel principle proved difficult to exploit. For low values of resistance the effects of lead and contact resistances could not be ignored and the resulting errors limited the accuracy of the measurements. Hamon discovered a way to realise and exploit a four-terminal resistor so that when a current is passed through any pair of leads there is zero voltage produced across the other two leads. Hamon discovered that a four-terminal junction can be realised simply by ensuring that three of the four leads to a junction block are symmetrical with respect to the fourth. Several successful geometries for the manufacture of the junction are known. U.S. Pat. No. 3,252,091 discloses one such geometry.
A four-terminal junction can be used to connect each of the (say, 10) resistors permanently in series in such a way that: firstly, each resistor is a well-defined four-terminal resistance; secondly, the resistance of the (say, 10) in series is exactly equal to the sum (of the 10) because the variable effects of the contact resistances are eliminated; and thirdly, with the use of a combining network as outlined below, it is possible to connect the (10) resistors in a parallel network such that the effects of the lead resistances is negligible.
Combining Networks: In order to make the parallel connection of the Hamon resistor, a low (but practically not zero) resistance connection must be made to each of the terminals of the (10) resistors. Because the resistance of the connection is not zero, the currents through each of the resistors may not be equal. If the currents are not equal then the measured value for the parallel resistance will be in error. The solution is to deliberately introduce known resistances in the various leads so that the current is shared equally. Because the four-terminal resistance is defined independently of the lead resistances, the combining network (also known as a compensation or sharing network) does not directly introduce any error. In practice, a combining network can be introduced into the current terminals or the voltage terminals with equal effect or in both for a greater effect. The sharing network principle was used by Kelvin in his double bridge--see U.S. Pat. No. 3,252,091, and was described in relation to the parallel connection of resistors by Brooks--see H B Brooks, Trans Amer Inst Elect Engrs, 39, p 549, 1920, and Wenner--see F Wenner and E Weibel, Bull Nat Bur Stand, 11, p 65, 1914, and is described by Kibble and Rayner--see B P Kibble and G H Rayner, "Coaxial AC Bridges", (Adam Hilger, Bristol) 1984 in more general terms.
The series-parallel build-up resistor (or Hamon resistor) described has been an important element of electrical metrology since Hamon described the idea. Many variants have been built and described with different numbers of resistors and simultaneous use of series and parallel combinations. The papers by Riley--see J C Riley, "The Accuracy of Series and Parallel Connections of Four-Terminal Resistors", IEEE Trans Instrum Meas, vol IM-16, pp 258-68, September 1967, Page--see C H Page, "Errors in the series-parallel build up of four-terminal resistors", J Res Nat Bur Stand Sect C, vol 69, pp 181-9, July/September 1965, Gorini--see I Gorini, "Errors in the Parallel Connection of a 100:1 Series-Parallel Build-up of Fourier-terminal Resistors", IEEE Trans Instrum Meas, vol IM-21, No. 3, August 1972, as well as Hamon describe the possible errors and their minimisation in the realisation of the Hamon resistors.
Commercially manufactured versions of the Hamon resistors are known to be produced by a number of companies including: Leeds and Northrup (Australia), who have followed Hamon's design in some detail; Guildline Instruments (Canada); and Electro Scientific Industries (USA).
The main use for Hamon resistors has been for the establishment of DC resistance standards at decade intervals, e.g. 1, 10, 100, 1000, 10000 ohms, etc. Measurements of the resistor for, say, the 1 ohm combination means that the value of the combination at the other values is also known. The main attribute of the resistors is the very high accuracy with which the resistance ratios can be realised (as good as 1 part in 100 000 000). Hamon resistors have also been used in pairs to establish accurate voltage ratios. Thompson--see A M Thompson, "Self checking Resistive Ratios", IEEE Trans Instr Meas, IM-27, 4, pp 423-5, December 1978, describes their application in general to the realisation of accurate voltage dividers. As with build-up resistors, the matching of equal valued resistors is critical to the performance of Hamon style voltage dividers.
All the Hamon networks have a large redundancy in the resistances realised i.e. some of the nominal resistance values can be realised by more than one series-parallel combination of the component resistors. Another disadvantage of Hamon networks, whether for build-up resistors or voltage dividers is that they are made with nominally equal valued resistances to exploit the Rayleigh principle, that is, to establish accurate ratios of resistance. Hamon networks are also made with the resistors connected permanently in series (in the so-called "ladder" form) so that two of the terminals of each of the four terminal junctions are used only as voltage or current terminals.